For three years, Republicans called on Senate Democrats to do a budget via regular order. Now that they’ve done so, neither side is enthusiastic about moving forward with a process to merge the House and Senate documents.

Senate Budget Chairwoman Patty Murray, D-Wash., and House Budget Chairman Paul D. Ryan, R-Wis., are in negotiations over the terms of a potential conference committee, meeting most recently on Wednesday. But outside their talks, rank-and-file members as well as leaders don’t seem very invested in the process.

Still, budget talks — if not a deal — could help House Republicans and Senate Democrats navigate this summer’s reprise of the debt limit debate.

Budgets are symbolic political documents, and the idea that Murray and Ryan could bridge the chasm between their respective spending blueprints, particularly when that product would not have the force of law, raises the question of whether either party is willing to sink political capital into the effort.

“There’s a better chance that Marco Rubio and Jay-Z will go on a concert tour this summer than there is [for] a conference agreement between Paul Ryan and Patty Murray,” one Senate aide said, referring to the Republican senator from Florida and the rapper.

The joint statement released after their meeting suggested Murray and Ryan are realistic about the dim prospects they face in trying to produce a mutually agreed-upon budget framework.

“We [recognize] the many differences between the House and Senate budget resolutions and the challenge we face in reaching an agreement,” the statement read. “We are committed to working to find common ground. We look forward to continuing the conversation as we move toward a conference committee.”

Sources tracking the talks said it was still too difficult to tell when the two might find an agreement on how to proceed to the conference, if they proceed at all. And other sources said the effort is tied to the upcoming debate over raising the debt ceiling.

Some Democratic aides are relying on President Barack Obama’s promise not to negotiate over the debt limit, but other Democrats and certainly Republicans believe a budget deal is needed as part of any agreement to extend the nation’s borrowing capacity.

A budget conference committee could be a venue to test out different ideas for that process. Some members have suggested that a conference committee could provide a shell for a larger budget compromise. Either way, whatever the conference did, it would need buy-in from leaders and the administration, and Republicans especially are fearful that won’t happen.

“There’s not much hope that there’s a final product that comes out of the conference committee unless that conference committee is a place holder that allows everybody to start all over,” one Senate Republican aide said. “Not one of these budgets is going to pass . . . so what’s the point of doing it? Once conferees are named, what’s the purpose of having that framework passed if there’s going to be no buy-in from leaderships?”

Moreover, a conference committee could expose rifts in both parties. Republicans likely would attack vulnerable in-cycle Democrats on tax increases while Democrats would use their oft-used charge that the GOP is aiming to destroy the social safety net. Plus, if an approved budget included reconciliation instructions for tax code changes, it could irk Senate Finance Chairman Max Baucus, D-Mont. Baucus has been working with his House GOP counterpart, Dave Camp of Michigan, on the issue for years and also has a history of bristling at those who cross over into Finance’s turf. At this point, though, sources see tax code changes being done outside the confines of the budget, if at all.

The whole affair has an air of futility. While the 2011 supercommittee on deficit reduction met, Murray — as co-chairwoman — was often frustrated because the Republicans with whom she was working had no buy-in from their caucus and little encouragement from leaders. Although sources close to Murray say she learned from her experience on that failed committee, it’s unclear whether the dynamics have shifted.

Additionally, her relationship with Ryan is still new — although he does have a good rapport with his House Budget counterpart, Chris Van Hollen of Maryland.

“That is the key question and that’s where we started — we don’t know whether that’s changed or not,” a senior Democratic aide said. “The question is not whether [Ryan] is likable; it’s whether he wants to cut a deal. We showed and the president showed that there’s a willingness to go pretty far to get a deal and we feel like that hasn’t been reciprocated.”